FA-6471 / Discrete calculus / Open access
Autocorrelation zero lag normalized · case 01
Sample count replaces zero-lag energy normalization.
ROOT CAUSE
Sample count replaces zero-lag energy normalization.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None
Unsuccessful approach: Truncated-tail energy changes the normalization across lags.
Case contract
Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. 0<=lag<=len(values); use the uncentered lagged product sum divided by full-signal energy. A zero-energy signal returns None. Exact operational definition: str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Discrete calculus results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(values, lag):
return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),len(values))) if values else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')
check('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3], 1) | 8/3 | 4/7 | Failed |
| fixture 2: ([1, 2, 3], 0) | 14/3 | 1 | Failed |
| fixture 3: ([2, 0], 1) | 0 | 0 | Passed |
| fixture 4: ([0, 0], 0) | 0 | None | Failed |
SHA-256 / 29648dc96cacc26002b2429bea359c23773dbfa227137cb2665179153c6e0e82
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(values, lag):
return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values[lag:]))) if any(values[lag:]) else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')
check('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3], 1) | 8/13 | 4/7 | Failed |
| fixture 2: ([1, 2, 3], 0) | 1 | 1 | Passed |
| fixture 3: ([2, 0], 1) | None | 0 | Failed |
| fixture 4: ([0, 0], 0) | None | None | Passed |
SHA-256 / fc18919c6065336e0606c21625abddcf073e60b278293a0e2ade05d470e3d2a3
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(values, lag):
return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')
check('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3], 1) | 4/7 | 4/7 | Passed |
| fixture 2: ([1, 2, 3], 0) | 1 | 1 | Passed |
| fixture 3: ([2, 0], 1) | 0 | 0 | Passed |
| fixture 4: ([0, 0], 0) | None | None | Passed |
SHA-256 / 010f1a0926edeb87553e2d0535e92d1d03ccb23e23b331868722b8623538a60c
Verification & scope
This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:38:02.414932+00:00.
Case digest / 4ea8b3be5bb2b3d1f4fcc7e75d128a5da427d12b6db1c187e78feb0bcf29e88b